How do you find the domain and range of $y = - \sqrt{x + 6} + 7$ $y = -sqrt(x+6)+7$ ?

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Answer 1 · 2018-06-19T05:34:32

The domain is $x \in [- 6, + \infty]$ $x in [-6,+oo]$ . The range is $y \in (- \infty, 7]$ $y in (-oo,7]$

The function is

$y = - \sqrt{x + 6} + 7$ $y=-sqrt(x+6)+7$

What's under the square root sign must be $\geq 0$ $>=0$

Therefore,

$x + 6 \geq 0$ $x+6>=0$

$\Rightarrow$ $=>$ , $x \geq - 6$ $x>=-6$

The domain is $x \in [- 6, + \infty]$ $x in [-6,+oo]$

When $x = - 6$ $x=-6$

$y = - \sqrt{- 6 + 6} + 7 = 0 + 7 = 7$ $y=-sqrt(-6+6)+7=0+7=7$

And when $x \to + \infty$ $x-> +oo$

$y \to (- \sqrt{+ \infty + 6} + 7) = - \infty$ $y->(-sqrt(+oo+6)+7)=-oo$

The range is $y \in (- \infty, 7]$ $y in (-oo,7]$

graph{-sqrt(x+6)+7 [-32.17, 71.9, -28.34, 23.65]}

How do you find the domain and range of y=−√x+6+7 y = -sqrt(x+6)+7 ?